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Weakly PIC1 Manifolds with Maximal Volume Growth

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Abstract

In this article we study the local estimates of Ricci flow when the curvature of the initial metric is of almost PIC1 and use it to study complete manifolds with weakly PIC1 and maximal volume growth.

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Acknowledgements

The authors would like to thank anonymous referees for helpful comments. The second author would like to thank his advisor Professor Luen-Fai Tam for his constant support and teaching over years.

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Authors and Affiliations

  1. School of Mathematical Science, Xiamen University, 422 S. Siming Rd., Xiamen, 361000, China

    Fei He

  2. Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL, 60208, USA

    Man-Chun Lee

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  1. Fei He
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  2. Man-Chun Lee
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Correspondence to Man-Chun Lee.

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F.H. was partially supported by the Fundamental Research Funds for the Central Universities Grant No. 20720180007, the National Natural Science Foundation of China No. 11801474 and Natural Science Foundation of Fujian Province No. 2019J05011.

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He, F., Lee, MC. Weakly PIC1 Manifolds with Maximal Volume Growth. J Geom Anal 31, 10868–10885 (2021). https://doi.org/10.1007/s12220-021-00667-4

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  • DOI: https://doi.org/10.1007/s12220-021-00667-4

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